NCERT Class 12 · Ch 3 Miscellaneous Exercise · Q5
NCERT Class 12 Maths · Chapter 3 Matrices · Miscellaneous Exercise Question 5
For A=\(\left[\begin{matrix}3 & 1\\-1 & 2\end{matrix}\right]\), prove A²−5A+7I=O.
💡 Concept Hints
- Check the matrix orders and the meaning of the requested operation before calculating.
- Keep row and column indices in order. Compare corresponding entries only after the matrix expressions have compatible dimensions.
✅ Step-by-Step Solution
Final Answer: The polynomial is O₂.
- A²=\(\left[\begin{matrix}8 & 5\\-5 & 3\end{matrix}\right]\).
- Compute −5A+7I=\(\left[\begin{matrix}-8 & -5\\5 & -3\end{matrix}\right]\).
- Their sum is \(\left[\begin{matrix}0 & 0\\0 & 0\end{matrix}\right]\), proving the identity.
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